A Procedure for Investigating the Liapunov Stability of Nonautonomous Linear Second-Order Systems

[+] Author and Article Information
S. E. Jones, T. R. Robe

Department of Engineering Mechanics, University of Kentucky, Lexington, Ky.

J. Appl. Mech 40(4), 1103-1106 (Dec 01, 1973) (4 pages) doi:10.1115/1.3423133 History: Received December 01, 1972; Online July 12, 2010


Utilizing Liapunov’s direct method a procedure is presented which generates sufficient conditions for the stability of the null solution of the nonautonomous differential equation ẍ + b(t)ẋ + a(t)x = 0. This procedure systematically leads to the construction of a Liapunov function for a given differential equation and thus eliminates the normally ad hoc nature of the direct method. Four examples illustrating the procedure are discussed.

Copyright © 1973 by ASME
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